PHYSICS PI NOTES 2024
Asia Yarlett
,
, NEWTONS LAWS
use of motion
& can
eq .
with New acceleration FsinG
Fy =
OH
* Can use work/Energy/Power -FA
O
FO
O
Fu =
* choose dir that block . moves as
surface
fk = MRN
It ↑
Copp dir .
mot )
.
O Ms tan P
=
my cos O L a
Cinclines
?
fXN : O IncreNdecr -fdeer Fgu mysino
=
Fg macos
OH &
=
Fg
fk Mk N Esmax
motion
Zone
=
friction
New force the rector of forces that
is 2 or
acting body
·
sum more on
no
motionf
Fnet ON
=
Fapplied
If the net force on an object is zero
,
the object will remain in a state of rest or keep movingIn a straight line at constant velocity
FnetXa
Fnet = m a . ad
in
Min
FAonB = -
FBonA
n
EQUILLIBRIUM :
Fnet = EF = ON
and measure)
any two objects in the universe attract eachother
&
& F =
G
MM
GRAVITATIONAL ACCELERATION (on surface)
Mi
if "F M2
&
F
18M
I r
I
s
FX m , M2
FX
(r)"
↳ =
ir (distance halves)
g
G gat
=
gam
↳Fur (distance doubles)
I&ndependant of m cobject)
:F
, MOTION
-
b = bi na)
x
-
=
20
GRAPHS OF MOTION
DISPLACEMENT -
TIME VELOCITY-TIME ACCELERATION -
TIME
gradient =
= Velocity
·
gradient D acceleration
: =
Are area = a xt = Ar velocity
area vxt displacement
·
·
: =
·
above or below r-axis
① ⑦
shows direction of relicly
① constant velocity
constant velocity
:
a =
0
Al V
C
B : Av
(m S")
S
(m) .
... = a =
Q
(M .
S
·
2)
t(s) t(s) t(s)
② constant acceleration (as o
①
Al
(m)
· (m S")
V
.
a
(M
C
.
S
·
2)
t(s) t(s) t(s)
③ constant deceleration (aco)
deceleration
Anper
a
Al ·
a G : neg . acceleration
V C
(m) (m S") (M S 2)
. ·
.
⑦
t(s)
t(s) t(s)
①star
⑦ direction accel dese o
standstill
SCENERIO : Ball B
dropped
,
-
55 after Ball A
-
projected
V ⑨
upwards ,
what time meet ?
t
② direction e - :
Cra =
kfB
I 0
L
xiA =
xiB = -S
AtB =
DE -
5
Dx = ViDt + EaDt2
initial velocity
given
an
simultaneous
·equation
· Free fall is motion under the influence of gravitational force only
res
.
Terminal velocity when air resistance equal magnitude to weight (oilstants
·
is in .
, "dropped
GRAPHS OF MOTION FOR VERTICAL
vi = 0
MOTION
as
crano
>
- constant acceleration
DISPLACEMENT -
TIME VELOCITY-TIME
gradient =
= Velocity ·
gradient D acceleration
: =
* Dr =
40 -
12
① ⑦ a
h for higher order questions shows direction of relicly
-
0
vi =
① #1 g Vf = -
case Ar = -
2
g 9 8m S
-
= -
,
↑+
.
start pf t(s)
t(s)
BR DV a = -
9, 8
(m) Cm S-
.
7
j ground = O
E - 9, 8
t(s)
+
Vi =
②
Case #2 · Vf
Ac
=
=
-
Vi
G
-
=
-
2
9 8m S
g = -
,
.
↑+
nina
AR
Av
①
= C
t
⑦ t
Start pr o 9, 8
=
S -
↑
* time
symmetry
Area = Sum o = Ax =
0
(cancel eachother out)
#3 ea
Vf
③
-
case
=
-
,
sm .
↑ +
9 8
a= ,
-
①
C
E t
Ar Dv
y
Start pr =
⑦ F - 9, 8
Area = same sign as large E
A
vi o
: "Douncing ball"
=
①
case #4 - each bounce =
separate projectile motion
↑+
butwhgene
i
~
O
F
11
a = 9 0
!
,
AR
A
Su · a
g
z ground= o
t
↳
At
when ball E t
In contact B E -
9, 8
with ground
when ball
In contact
with ground
Area = Du = displacement from
starting position
&
*
change
EQUATIONS Of MOTION CAN BE USED WHEN Acceleration
·
rate of
⑧ constant acceleration
motion
of relocity
·
linear/straight-line
=
a
· constant Fret (therefore constant acceleration)
, MOMENTUM B IMPULSE
MOMENTUM
p =
m .
v
(kg . m .
S") //N S) .
E
(P)
change In A momentum Pf.
/ <kg S') same dir
I
As
IMPULSE (N S) . . m .
Impulse = .
momentum · p incr In . same dir :
Ap Fret Xp
Do
=
.
At -p =
Pis
Fret. At Pf-Pi Pf
St)
=
CHANGE IN MOMENTUM (kg . M .
Pf Ener At m Dv
Ap
=
Pi p dear dir.:
.
= .
in same
-
·
Di
N S M S-
=
kg
.
mus-Mui
ups
.
=
.
po"
= m (vo -
vi)
Area
Ins y
F ·
p changes dir :
= m .
AV
Pr Pi
sa
&
Ap
AB"
-
"fnet of t(s)
values
NEWTONS SECOND LAW IN TERMS OF MOMENTUM
Fret Ap
I
=
At
fuerd A
PC -
Pi (constanta
=
At
Fuel Fuel
=
m Av
but
·
-
At
a
the
t At
: Fnet = m . a
nu
& net force that the momentum
changes
PRINCIPLE CONSERVATION OF LINEAR MOMENTUM
Epi =
Eph p is constant
,
but
- distribution of P
Pai +
Pri =
Pact PBC can change
Marai +
MgVgi
=
MaVaf + My VBf
CLASTIC OR INFLASTIC (kinetic energy)
Eki Elf frictionless b no height
=Ma (at)?+ Mrs (Visf)2
2
= EMA(Vai) [MB (VBi) + .. EK conserved
Joules = Joules (no loss (
energy
=
if thi =
fkf elastic collision
3
:
don't begin eg
. With this expression
If fki fet : melastic collision
, P =
m v
.
Fret =
Pat
Ap fnet At
= .
NOT change in momentum X
Epi =
Epf
&
(
Elastic collision which both total momentum and total
· :
Collision in
Kinetic are conserved
energy
, WORK ,
ENERGY ,
POWER
WORK SCALAR
The work done by equal to of
on an object a constant force is FX Drxcoso where F is the magnitude
the force the magnitude of the displacement and O the between F and Ac .
,
Are is Is
angle
L
(magnitude ( ~ angle between force and displacement
-
(makes provision for # or E
Scalar &G indicate energy transferred W T Ac CosO
=
: .
.
or removed (NOT direction) J ↑
M O
N m
Ekg
.
.
m . s -
DETERMINING O between F & Ax :
D F} Bu same direction ② opposite direction ③ Perpendicular (FAx)
0 180
=
=0
arictionen WA
f Di FO
W = FACCOSO Upp . direct .
=
#Dr (S (180) Wr =
F Bu COS (90)
= I - I
of motion =
g
= FBx -
=
fAl =
OJ
energy gained energy lost
>
- >
-
>
-
no work is done as its
>
- W > O (max) >
- WLO perpendicular to dir .
of mot.
leg. Object dropped+ Fg)( leg. object thrown upwards)
① at an
angle FY
⑤ on an incline
Fr Wig Fg Br CosO
W =
w
Fu Are cosO =
Fare/ Fg sing
F As Los (0) FgcuS
Fgy/
=
FgB Cost
=
=
+
= I
A m
FLOS
Bangle
=
Di
FgUe--"
"orgy
Du
COS (0)
of inclination BBre .
.
,
Force has
=
I
i Du
a component all forces do work
↑
1
:
m
=
.
g Sing
. Ar
NET WORK (Whet =
2 W) WORK DONE BY FORCES IN EQUILIBRIUM
Wa FAce Du CusO FLOSS AU COSO "Constant wello city" a =
g : Atk 0
·
= = =
. .
. .
fk FA
3.
-
=
Ww =
N Ac (US (90) O object not plane Dr : FA fl
·
=
.
. on same as =
: no work is done
Fg (90) :
( f()
)3
COS Fret fa G
Ng Br G
=
+ =
·
= -
.
. =
newton
N (tp ? =
·
Wf =
f .
Du . Cos(180) =
-
FAR FA Whet =
Wa + (wk) =
0
18 Fas
: Whet =
Wa + ( Wf) fe
...
Y
-
"
or Eg' Dis DISTANCE "travelled for 5s & 5 m S-1 .
Whet =
Fret DC cosO : Du =
5 x 5 :
2Sm
↳ 0 =
00 or 188 .
If
↓
>
-
Wher = W to overcome Eg : a = 0 ... Whet = 0J
Ener Bx . .
COSO
no Force
En
ifnodisplacemena ndicular
no work is done
Whet
DEk (frictionless
Wo + Wha
, MECHANICAL
ENERGY
ability to do work
Eg .
of motion :
(linear motion
only
↑ energy of motion tk
: EmrC
vf 2 =
vi2 + 2aDu
EM =
Ek + Ep ↓ e
-
energy due to position Ep =
migh
a
:
PRINCIPLE CONSERVATION OF MECHANICAL ENERGY (only conservative forces present/ isolated systems)
notimme Mi =
EM- Total mechanical
energy in an Isolated system remains constant t
data
Ek ;Epi + =
Ekf +
Epf & Nnc Dep
=
+
Atk -
sheet
-
>
- use with
-
(EKC-fki) =
EpC-Epi none
CURVED surface
⑧ =
DEP#
-
Atk =
Dep
Atk Dep
① Pendulum
-
② Roller
=
coaster
M - ↓ fictionless
& Emi = EEMS
③ Free-fall
EPmu
WORK -
ENERGY THEOREM (external forces -
use If height NOT
given )
Whet =
Atk >
-
Net work done on an object is equal to the
change in its kinetic energy
Fnet .
Br cosO = mr2 +
.
-
[mu2; (caut use this formula on a curve as no angle)
or Sh
If Ath 0J
Wher W to overcome
Fg a 0
>
- = . = :. =
dependant on path taken
NON-CONSERVATIVE FORIES (external forces -
use It height given
I I &
Whc =
DEM isolated system : Wnc =
0 ·
friction
A
s removes
OEM
DER
or
Whc = + Afp :
Dep + AEk =
0 ·
applied force
from object
Dem =
Atk +
DEp Atp = -Atk ·
tension
CONSERVATIVE FORCE : Independant of path taken
WFg =
Ep &
=
Fg bu Cos ou
"constant velocity" :: AEK =
0
:=
mgh 3 em remains unchanged "travelled for 55 & 5m S"" .
=
3x5 :
3
force of DR
·
gravity A H
sinO =
Du 70
POWER
rate at which work is done/energy transferred
F Ax 200 v is constant
Not p
.
.
= >
-
p - At = v same dir.... 0 =
·
0
↓
Watt (w) <w =
1 J st .
=
Fu(1)
: Pare =
F . Vare
, W = F DK
.
.
cosO
[
J Whet = AEk
Emi = EME
p =
Asia Yarlett
,
, NEWTONS LAWS
use of motion
& can
eq .
with New acceleration FsinG
Fy =
OH
* Can use work/Energy/Power -FA
O
FO
O
Fu =
* choose dir that block . moves as
surface
fk = MRN
It ↑
Copp dir .
mot )
.
O Ms tan P
=
my cos O L a
Cinclines
?
fXN : O IncreNdecr -fdeer Fgu mysino
=
Fg macos
OH &
=
Fg
fk Mk N Esmax
motion
Zone
=
friction
New force the rector of forces that
is 2 or
acting body
·
sum more on
no
motionf
Fnet ON
=
Fapplied
If the net force on an object is zero
,
the object will remain in a state of rest or keep movingIn a straight line at constant velocity
FnetXa
Fnet = m a . ad
in
Min
FAonB = -
FBonA
n
EQUILLIBRIUM :
Fnet = EF = ON
and measure)
any two objects in the universe attract eachother
&
& F =
G
MM
GRAVITATIONAL ACCELERATION (on surface)
Mi
if "F M2
&
F
18M
I r
I
s
FX m , M2
FX
(r)"
↳ =
ir (distance halves)
g
G gat
=
gam
↳Fur (distance doubles)
I&ndependant of m cobject)
:F
, MOTION
-
b = bi na)
x
-
=
20
GRAPHS OF MOTION
DISPLACEMENT -
TIME VELOCITY-TIME ACCELERATION -
TIME
gradient =
= Velocity
·
gradient D acceleration
: =
Are area = a xt = Ar velocity
area vxt displacement
·
·
: =
·
above or below r-axis
① ⑦
shows direction of relicly
① constant velocity
constant velocity
:
a =
0
Al V
C
B : Av
(m S")
S
(m) .
... = a =
Q
(M .
S
·
2)
t(s) t(s) t(s)
② constant acceleration (as o
①
Al
(m)
· (m S")
V
.
a
(M
C
.
S
·
2)
t(s) t(s) t(s)
③ constant deceleration (aco)
deceleration
Anper
a
Al ·
a G : neg . acceleration
V C
(m) (m S") (M S 2)
. ·
.
⑦
t(s)
t(s) t(s)
①star
⑦ direction accel dese o
standstill
SCENERIO : Ball B
dropped
,
-
55 after Ball A
-
projected
V ⑨
upwards ,
what time meet ?
t
② direction e - :
Cra =
kfB
I 0
L
xiA =
xiB = -S
AtB =
DE -
5
Dx = ViDt + EaDt2
initial velocity
given
an
simultaneous
·equation
· Free fall is motion under the influence of gravitational force only
res
.
Terminal velocity when air resistance equal magnitude to weight (oilstants
·
is in .
, "dropped
GRAPHS OF MOTION FOR VERTICAL
vi = 0
MOTION
as
crano
>
- constant acceleration
DISPLACEMENT -
TIME VELOCITY-TIME
gradient =
= Velocity ·
gradient D acceleration
: =
* Dr =
40 -
12
① ⑦ a
h for higher order questions shows direction of relicly
-
0
vi =
① #1 g Vf = -
case Ar = -
2
g 9 8m S
-
= -
,
↑+
.
start pf t(s)
t(s)
BR DV a = -
9, 8
(m) Cm S-
.
7
j ground = O
E - 9, 8
t(s)
+
Vi =
②
Case #2 · Vf
Ac
=
=
-
Vi
G
-
=
-
2
9 8m S
g = -
,
.
↑+
nina
AR
Av
①
= C
t
⑦ t
Start pr o 9, 8
=
S -
↑
* time
symmetry
Area = Sum o = Ax =
0
(cancel eachother out)
#3 ea
Vf
③
-
case
=
-
,
sm .
↑ +
9 8
a= ,
-
①
C
E t
Ar Dv
y
Start pr =
⑦ F - 9, 8
Area = same sign as large E
A
vi o
: "Douncing ball"
=
①
case #4 - each bounce =
separate projectile motion
↑+
butwhgene
i
~
O
F
11
a = 9 0
!
,
AR
A
Su · a
g
z ground= o
t
↳
At
when ball E t
In contact B E -
9, 8
with ground
when ball
In contact
with ground
Area = Du = displacement from
starting position
&
*
change
EQUATIONS Of MOTION CAN BE USED WHEN Acceleration
·
rate of
⑧ constant acceleration
motion
of relocity
·
linear/straight-line
=
a
· constant Fret (therefore constant acceleration)
, MOMENTUM B IMPULSE
MOMENTUM
p =
m .
v
(kg . m .
S") //N S) .
E
(P)
change In A momentum Pf.
/ <kg S') same dir
I
As
IMPULSE (N S) . . m .
Impulse = .
momentum · p incr In . same dir :
Ap Fret Xp
Do
=
.
At -p =
Pis
Fret. At Pf-Pi Pf
St)
=
CHANGE IN MOMENTUM (kg . M .
Pf Ener At m Dv
Ap
=
Pi p dear dir.:
.
= .
in same
-
·
Di
N S M S-
=
kg
.
mus-Mui
ups
.
=
.
po"
= m (vo -
vi)
Area
Ins y
F ·
p changes dir :
= m .
AV
Pr Pi
sa
&
Ap
AB"
-
"fnet of t(s)
values
NEWTONS SECOND LAW IN TERMS OF MOMENTUM
Fret Ap
I
=
At
fuerd A
PC -
Pi (constanta
=
At
Fuel Fuel
=
m Av
but
·
-
At
a
the
t At
: Fnet = m . a
nu
& net force that the momentum
changes
PRINCIPLE CONSERVATION OF LINEAR MOMENTUM
Epi =
Eph p is constant
,
but
- distribution of P
Pai +
Pri =
Pact PBC can change
Marai +
MgVgi
=
MaVaf + My VBf
CLASTIC OR INFLASTIC (kinetic energy)
Eki Elf frictionless b no height
=Ma (at)?+ Mrs (Visf)2
2
= EMA(Vai) [MB (VBi) + .. EK conserved
Joules = Joules (no loss (
energy
=
if thi =
fkf elastic collision
3
:
don't begin eg
. With this expression
If fki fet : melastic collision
, P =
m v
.
Fret =
Pat
Ap fnet At
= .
NOT change in momentum X
Epi =
Epf
&
(
Elastic collision which both total momentum and total
· :
Collision in
Kinetic are conserved
energy
, WORK ,
ENERGY ,
POWER
WORK SCALAR
The work done by equal to of
on an object a constant force is FX Drxcoso where F is the magnitude
the force the magnitude of the displacement and O the between F and Ac .
,
Are is Is
angle
L
(magnitude ( ~ angle between force and displacement
-
(makes provision for # or E
Scalar &G indicate energy transferred W T Ac CosO
=
: .
.
or removed (NOT direction) J ↑
M O
N m
Ekg
.
.
m . s -
DETERMINING O between F & Ax :
D F} Bu same direction ② opposite direction ③ Perpendicular (FAx)
0 180
=
=0
arictionen WA
f Di FO
W = FACCOSO Upp . direct .
=
#Dr (S (180) Wr =
F Bu COS (90)
= I - I
of motion =
g
= FBx -
=
fAl =
OJ
energy gained energy lost
>
- >
-
>
-
no work is done as its
>
- W > O (max) >
- WLO perpendicular to dir .
of mot.
leg. Object dropped+ Fg)( leg. object thrown upwards)
① at an
angle FY
⑤ on an incline
Fr Wig Fg Br CosO
W =
w
Fu Are cosO =
Fare/ Fg sing
F As Los (0) FgcuS
Fgy/
=
FgB Cost
=
=
+
= I
A m
FLOS
Bangle
=
Di
FgUe--"
"orgy
Du
COS (0)
of inclination BBre .
.
,
Force has
=
I
i Du
a component all forces do work
↑
1
:
m
=
.
g Sing
. Ar
NET WORK (Whet =
2 W) WORK DONE BY FORCES IN EQUILIBRIUM
Wa FAce Du CusO FLOSS AU COSO "Constant wello city" a =
g : Atk 0
·
= = =
. .
. .
fk FA
3.
-
=
Ww =
N Ac (US (90) O object not plane Dr : FA fl
·
=
.
. on same as =
: no work is done
Fg (90) :
( f()
)3
COS Fret fa G
Ng Br G
=
+ =
·
= -
.
. =
newton
N (tp ? =
·
Wf =
f .
Du . Cos(180) =
-
FAR FA Whet =
Wa + (wk) =
0
18 Fas
: Whet =
Wa + ( Wf) fe
...
Y
-
"
or Eg' Dis DISTANCE "travelled for 5s & 5 m S-1 .
Whet =
Fret DC cosO : Du =
5 x 5 :
2Sm
↳ 0 =
00 or 188 .
If
↓
>
-
Wher = W to overcome Eg : a = 0 ... Whet = 0J
Ener Bx . .
COSO
no Force
En
ifnodisplacemena ndicular
no work is done
Whet
DEk (frictionless
Wo + Wha
, MECHANICAL
ENERGY
ability to do work
Eg .
of motion :
(linear motion
only
↑ energy of motion tk
: EmrC
vf 2 =
vi2 + 2aDu
EM =
Ek + Ep ↓ e
-
energy due to position Ep =
migh
a
:
PRINCIPLE CONSERVATION OF MECHANICAL ENERGY (only conservative forces present/ isolated systems)
notimme Mi =
EM- Total mechanical
energy in an Isolated system remains constant t
data
Ek ;Epi + =
Ekf +
Epf & Nnc Dep
=
+
Atk -
sheet
-
>
- use with
-
(EKC-fki) =
EpC-Epi none
CURVED surface
⑧ =
DEP#
-
Atk =
Dep
Atk Dep
① Pendulum
-
② Roller
=
coaster
M - ↓ fictionless
& Emi = EEMS
③ Free-fall
EPmu
WORK -
ENERGY THEOREM (external forces -
use If height NOT
given )
Whet =
Atk >
-
Net work done on an object is equal to the
change in its kinetic energy
Fnet .
Br cosO = mr2 +
.
-
[mu2; (caut use this formula on a curve as no angle)
or Sh
If Ath 0J
Wher W to overcome
Fg a 0
>
- = . = :. =
dependant on path taken
NON-CONSERVATIVE FORIES (external forces -
use It height given
I I &
Whc =
DEM isolated system : Wnc =
0 ·
friction
A
s removes
OEM
DER
or
Whc = + Afp :
Dep + AEk =
0 ·
applied force
from object
Dem =
Atk +
DEp Atp = -Atk ·
tension
CONSERVATIVE FORCE : Independant of path taken
WFg =
Ep &
=
Fg bu Cos ou
"constant velocity" :: AEK =
0
:=
mgh 3 em remains unchanged "travelled for 55 & 5m S"" .
=
3x5 :
3
force of DR
·
gravity A H
sinO =
Du 70
POWER
rate at which work is done/energy transferred
F Ax 200 v is constant
Not p
.
.
= >
-
p - At = v same dir.... 0 =
·
0
↓
Watt (w) <w =
1 J st .
=
Fu(1)
: Pare =
F . Vare
, W = F DK
.
.
cosO
[
J Whet = AEk
Emi = EME
p =
